Combustors are commonly used in industrial and commercial operations to ignite fuel to produce combustion gases having a high temperature and pressure. For example, gas turbines and other turbomachines typically include one or more combustors to generate power or thrust. A typical gas turbine used to generate electrical power includes an axial compressor at the front, multiple combustors around the middle, and a turbine at the rear. Ambient air enters the compressor as a working fluid, and the compressor progressively imparts kinetic energy to the working fluid to produce a compressed working fluid at a highly energized state. The compressed working fluid exits the compressor and flows through one or more fuel injectors in the combustors where the compressed working fluid mixes with fuel before igniting to generate combustion gases having a high temperature and pressure. The combustion gases flow to the turbine where they expand to produce work. For example, expansion of the combustion gases in the turbine may rotate a shaft connected to a generator to produce electricity.
At particular operating conditions, combustion dynamics at specific frequencies and with sufficient amplitudes, which are in phase and coherent, may produce undesirable sympathetic vibrations in the turbine and/or other downstream components. In the context of this invention, coherence refers to the strength of the linear relationship between two (or more) dynamic signals, which is strongly influenced by the degree of frequency overlap between them. Coherence provides a measure of the degree of modal coupling of the combustion dynamics.
An alternate quantification for modal coupling is the standard deviation of the combustion dynamics frequency, either from combustor to combustor or through time. The standard deviation of the combustion dynamics frequency from combustor to combustor, herein referred to as the “standard deviation of the frequency” provides a measure of the variation in combustion dynamics frequency from combustor to combustor, which correlates with the coherence of the combustion instability. The standard deviation of the combustion dynamics frequency through time, herein referred to as the “standard deviation of the frequency through time” provides a measure of the variation of the combustion dynamics frequency through time, which also correlates with the coherence of the combustion instability. As the variation in frequency, either from combustor to combustor or through time, increases, the coherence decreases. Therefore, standard deviation of the frequency of the combustion dynamics, either from combustor to combustor or through time, can be used in the place of coherence to detect modal coupling of the combustion dynamics. Although not as robust, the standard deviation of amplitude, either from combustor to combustor or through time, herein referred to as “standard deviation of amplitude” and “standard deviation of amplitude through time,” respectively, can also be used in place of coherence to detect modal coupling of the combustion dynamics.
Alternative quantities, which are variations of standard deviation, can also be used in place of coherence to detect modal coupling. These include the variance (the square of the standard deviation of the frequency), the variance through time (the square of the standard deviation of the frequency through time), the coefficient of variation of frequency (the standard deviation of the frequency normalized by the mean of the frequency), the coefficient of variation of frequency through time (the standard deviation of the frequency through time normalized by the mean of the frequency through time), the index of dispersion of the frequency (the variance of the frequency normalized by the mean of the frequency) and the index of dispersion of the frequency through time (the variance of the frequency through time normalized by the mean of the frequency through time).
Typically, the problem of combustion-driven responses of downstream components is managed by combustor tuning which limits the amplitude of the combustion dynamics in a particular frequency band. However, combustor tuning may unnecessarily limit the operating range of the combustor. An alternative approach to reducing unwanted combustion-driven responses of downstream components is to alter the frequency, phase, amplitude, standard deviation of frequency, standard deviation of frequency through time, coefficient of variation of frequency, coefficient of variation of frequency through time, index of dispersion of frequency, index of dispersion of frequency through time, variance of frequency, and/or variance of frequency through time of the combustion dynamics.
For instance, as the combustion instability frequency in one or more, but not all, combustors is driven away from that of the other combustors, coherence and, therefore, modal coupling of combustion dynamics is reduced, which thereby reduces the ability of the combustor tone to cause a vibratory response in downstream components. Alternatively, shifting the combustion dynamics frequency of each of the combustors away from the natural frequency of the downstream components may also reduce unwanted vibrations of downstream components.
Therefore, a system and method for operating a gas turbine that detects and/or reduces the unwanted vibrations in downstream components by altering the frequency, phase, amplitude, standard deviation of the frequency, standard deviation of the frequency through time, coefficient of variation of the frequency, coefficient of variation of the frequency through time, index of dispersion of the frequency, index of dispersion of the frequency through time, variance of the frequency, and/or variance of the frequency through time of the combustors would be useful for enhancing the thermodynamic efficiency of the combustors, protecting against accelerated wear, promoting flame stability, and/or reducing undesirable emissions over a wide range of operating levels, without detrimentally impacting the life of the downstream hot gas path components.